This book is about the distribution of chemical elements in the sea and the processes that control it. We address the questions: What controls the mean abundance of the elements? What controls their variation in space? What controls changes in time (for example during ice ages)? The primary focus is on those elements for which ‘‘biological processes’’ is part of the answer, the main example naturally being carbon. The whole subject is in a state of active research, and this book will highlight important growing points. It will concentrate more on how we know than on what, thereby introducing readers to the tools with which they can add to our knowledge of ocean biogeochemistry.
The approach of this book combines two principles. First, measurements of the concentration of dissolved
1.1 Chemical Composition of the Ocean
Table 1.1.1 and figure 1.1.1 show the mean concentrations of chemical elements and a few compounds in the ocean (ignoring the elements in water molecules, hydrogen and hydroxyl ions, including only dissolved O2, and including dissolved N2 as well as nitrate). The mean oceanic concentration of the elements ranges over almost 12 orders of magnitude. At the low end are some of the rare earth elements with concentrations of order 1 nmol m�3, for example, elements 67, 69, and 71 (holmium, thulium, and lutetium). At the high end is chlorine, with a concentration of almost 600 mol m�3.
We discuss here three different hypotheses for what controls the composition of the ocean. The first two are the accumulation hypothesis and the kinetic control hypothesis. The accumulation hypothesis proposes that the oceanic concentrations represent simply the accumulated inflow from rivers since the ocean came into existence. The kinetic control hypothesis proposes that the composition of the ocean results from a balance between the input to the ocean from external sources and the rate of removal, with many of the removal
inorganic chemicals are among the most accurate we can make in the ocean. Therefore, we will generally start with these data and ask what needs to be explained. Possible explanations will arise from a variety of sources including many direct observations of processes. The second basic principle will be to express these qualitative explanations in terms of quantitative modelsofprocesses thatmakepredictionsthatcanbecompared with the observations. We then return to the data to assess how accurate the predictions, and therefore the models, are.
In the following section we make our approach more concrete by taking a first look at perhaps the most important question in chemical oceanography: What controls the mean chemical composition of the ocean?
processes being biologically driven. We will test each of these hypotheses by building simple models of them and using observations to see if the predictions of the models are consistent with what we know of the ocean. The third hypothesis that we discuss is the equilibrium hypothesis, which proposes that the oceanic composition is controlled by equilibria between seawater and chemical precipitates from seawater, the solid particles of continental origin that sink though the water column and accumulate in the sediments, and the oceanic crust that underlies the ocean.
A first obvious guess at what determines oceanic concentrations is that they represent simply the accumulated inflow from rivers since the ocean came into existence. The contrast between the high oceanic and low river concentrations of the elements (see table 1.1.1) clearly suggests that accumulation is occurring in the ocean, but can it explain the observed concentrations? Let us develop a mathematical description of how the oceanic mean concentration of an element A (which we denote alternatively by Coc or [A] in units of mmol m�3)
1
Introduction
Table 1.1.1 Continued
Ocean River Dissolved Atomic Concentration Concentration ta and tr
Z Element Weight (mmol m�3) (mmol m�3) (yr)
52 Tellurium Te 127.6 53 Iodine I 126.905 480 54 Xenon Xe 131.29 0.5 55 Cesium Cs 132.905 0.002 0.26 300 56 Barium Ba 137.33 87 400 8,000 57 Lanthanum La 138.906 0.03 0.4 3,000 58 Cerium Ce 140.12 0.03 0.6 2,000 59 Praseodymium Pr 140.908 0.004 0.05 3,000 60 Neodymium Nd 144.24 0.03 0.3 4,000 61 Promethium Pm (145) 62 Samarium Sm 150.36 0.004 0.05 3,000 63 Europium Eu 151.96 0.001 0.007 5,000 64 Gadolinium Gd 157.25 0.005 0.05 4,000 65 Terbium Tb 158.3925 0.001 0.006 6,000 66 Dysprosium Dy 165.5 0.006 67 Holmium Ho 164.93 0.001 0.006 6,000 68 Erbium Er 167.26 0.006 0.02 10,000 69 Thulium Tm 168.934 0.001 0.006 6,000 70 Ytterbium Yb 173.04 0.005 0.02 9,000 71 Lutetium Lu 174.967 0.001 0.006 6,000 72 Hafnium Hf 178.49 <0.05 73 Tantalum Ta 180.948 <0.014 74 Tungsten W 183.85 <0.006 75 Rhenium Re 186.207 0.02 76 Osmium Os 190.2 77 Iridium Ir 192.22 78 Platinum Pt 195.08 79 Gold Au 196.967 0.057 0.01 200,000 80 Mercury Hg 200.59 0.031 81 Thallium Tl 204.383 0.060 82 Lead Pb 207.2 0.005 5 40 83 Bismuth Bi 208.98 0.05 84 Polonium Po (209) 85 Astatine At (210) 86 Radon Rn (222) 87 Francium Fr (223) 88 Radium Ra 226.025 89 Actinium Ac 227.028 90 Thorium Th 232.038 <0.003 0.4 300 91 Protactinium Pa 231.036 92 Uranium U 238.029 14 0.17 2,800,000
will change with time. The total number of moles of this element in the ocean is the product of its mean oceanic concentration multiplied by the oceanic volume, Voc
(m3). The time rate of change of the total number of moles of this element, dMA =dt, is equal to the sum of all oc inputs and losses of this element, i.e.,
dMA dVocCococ
dt ¼
dt ¼ inputs � losses (1:1:1)
In the case of the accumulation hypothesis, we assume that there are no losses. We further assume that the inputs are controlled only by the addition of element A by rivers, which we estimate by taking the product of river flow nriver (m3 yr�1) and river concentration of the element, Criver. This gives:
Figure 1.1.1: A graphical illustration of the dissolved concentrations of elements and some compounds expressed
as log to the base 10 [ Johnson and Jannasch, 1994]. The higher concentration elements are given on the right-hand
side and the lower concentration elements are given on the left-hand side. The bars represent the range of
concentrations in the ocean. The full range of concentrations covers almost 12 orders of magnitude.
We take Voc out of the time-derivative assuming that the oceanic volume has remained constant through time. This differential equation has the solution
Coc(t)�Coc(t¼0) ¼ nriver
V
� oc
Criver � Dt (1:1:3)
for the change in concentration in the time interval Dt between t and t ¼ 0. If we assume that the ocean came into being at t ¼ 0 as essentially fresh water, i.e., Coc(t ¼ 0) ¼ 0, we obtain
Coc (t)¼ nriver
V
� oc
Criver � Dt (1:1:4)
This equation predicts that today’s mean ocean concentration of any element A is directly proportional to its river concentration Criver, and hence that the ratio of various elements in the ocean should be equal to the ratio of these elements in rivers. Rather than testing for this particular prediction, we infer for each element an accumulation age, ta ¼ Dt, which represents a time in the past when, given today’s river input and ocean mean concentration, the oceanic mean concentration of this element must have been zero. If the accumulation hypothesis is correct, then we expect this age to (i) reflect the age of the ocean, and (ii) be equal for all elements. We obtain ta, the number of years of accumulation that the present concentration and river
4
inflow represent, by rearranging (1.1.4):
Voc Coc 1:29�1018 m3 Cocta ¼ nriver
� Criver
¼ 3:7�1013 m3 yr�1
� Criver (1:1:5)
Coc ¼ 34,500 yr � Criver
where we inserted today’s Voc (1.29�1018 m3) and nriver (3.7�1013 m3 yr�1). Both Coc and Criver are given in table 1.1.1. The river concentration shown in the table is for the dissolved component only, not including any suspended material, which we assume is mostly removed before getting into the open ocean. Note that the above river flow includes a direct groundwater discharge of *6% [Berner and Berner, 1987].
Looking at the accumulation times shown in the last column of table 1.1.1, we are struck by two things. (1) All of the accumulation times are at least a factor of 30 less than what we think the age of the ocean is (3.85 billion years). (2) The accumulation times for different elements vary by almost eight orders of magnitude. As this is in strong violation of our prediction on the basis of the accumulation hypothesis, we conclude that this hypothesis is unlikely to be correct. An alternative interpretation, that the river input of elements was smaller in the past, is the opposite of what we might expect, given that the removal of chemicals from land would gradually deplete the land of those chemicals.
We therefore turn to the kinetic control hypothesis, which considers removal as well as addition of elements to the mean ocean. We modify (1.1.2) by adding a removal term, R, in mol yr�1.
dCocVoc � dt
¼ nriver � Criver � R (1:1:6)
This model is illustrated in figure 1.1.2. Given that the accumulation times we previously calculated are much shorter than the age of the ocean, it might be reasonable to suppose that the ocean concentrations have achieved a steady state, i.e., that dCoc/dt ¼ 0. We see from (1.1.6) that this implies that removal is in equilibrium with addition by rivers. Unfortunately, the steady-state solution of (1.1.6), R ¼ nriver � Criver , does not solve our problem of determining what controls the ocean concentration, since all it says is that the removal equals the input without specifying what the removal mechanism is. In order to solve this problem we need to specify how R is related to the concentration Coc .
The easiest and most common approach that geochemists take in solving a box model such as the above is to assume that R is linearly proportional to the concentration in the water, i.e.,
R ¼ Voc � k � Coc (1:1:7)
where k (yr�1) is the rate constant for the removal and where we included Voc to account for the fact that R
Introduction
CONTINENTS νriver · Criver
Coc = mean ocean concentration
Voc = ocean volume
∂(Coc ·Voc)
∂t = νriver · Criver - R
R
SEDIMENTS
OCEAN
Figure 1.1.2: Schematic illustration of a one-box model of the ocean
with river input and a removal term R
reflects the whole ocean removal. Chemists refer to reactions such as this as being first order in the concentration. Substituting (1.1.7) into (1.1.6) and dividing by Voc gives:
dC
dtoc ¼
nriver � Criver � k � Coc (1:1:8)Voc
In a steady state it is easy to solve (1.1.8) for the ocean concentration:
Coc ¼ 1
k � nriver � Criver
(1:1:9)Voc
We show in panel 1.1.1 that this steady-state concentration is achieved with a characteristic time constant tr, which is determined by the inverse of the rate constant k, i.e.,
1 tr ¼
k (1:1:10)
Elements whose removal timescale is very fast, i.e., whose k is large, will therefore tend to have a fast response time after a perturbation and quickly recover their new steady-state concentration. The opposite is the case for slowly reacting elements, i.e., those with a small k. It turns out that this characteristic response time, tr , is mathematically identical to the accumulation time, ta,
5
Chapter 1
(solve (1.1.9) for 1/k and insert it into (1.1.10)), so that the last column of table 1.1.1 actually represents both tr and ta although it is more appropriate to think of the former as representing a residence time of the chemical with respect to the addition by rivers and removal by reaction R.
We now have a model of what controls the ocean concentration with a steady-state solution given by (1.1.9). This equation tells us that for a constant removal rate constant k and ocean volume Voc , there is a linear relationship between concentration and river input. For example, a doubling of the river input would lead to a doubling of concentration. Similarly, for constant river input, there is an inverse linear dependence on the removal rate constant. A halving of the removal rate constant (slower removal) would double the ocean concentration. Our model thus explains the wide range of concentrations in table 1.1.1 as resulting in part from differences in the river concentrations, but primarily from variations in the removal rate constant k. Our model also enables us to predict how the ocean might respond to changes in time. Panel 1.1.1 gives two examples of analytical solutions to the time-dependent equation (1.1.8) that show how the ocean would adjust to an abrupt or cyclic change in the river input.
The reader should keep in mind that (1.1.9) applies to removal of tracer by first-order processes, in other words, to removal processes that are directly proportional to the concentration of the tracer. While simple models such as this provide powerful insights into oceanic processes that we shall return to again and again, one should keep in mind that actual removal processes may have a more complex behavior than this, as we shall see in subsequent chapters.
Our analysis demonstrates the crucial role of the removal mechanisms and rate constants in controlling the chemical concentrations. The assumption that the removal of a chemical is first order in its concentration is essentially an assumption that the concentration is controlled by kinetics. An alternative approach, explored in a seminal paper published by the Swedish chemist Sill�e [1961], is that ocean concentrations are deter-en mined instead by thermodynamic equilibria between seawater and mineral phases. In such a model, the chemical composition would remain constant through time at the equilibrium concentration Cequilibrium, i.e., Coc ¼ Cequilibrium. This is in contrast to our kinetic model (which is similar to the one developed by Broecker in his response to Sillen’s proposal [Broecker, 1971]), which permits ocean concentrations to vary in response to changes in the river input and the removal rate constant.
Many of the inorganic chemical equilibria proposed by Sillen and others play an important role in influencing ocean chemical composition. However, observations show that seawater is usually undersaturated with respect to minerals found in deep-sea sediments. Furthermore, many of the postulated mineral phases either do not exist or are insufficient to explain the removal rate required to balance the river inflow. The evidence is thus very strong that the removal processes generally involve a more complex blend of biological, chemical, and geological processes such as the formation of evaporation basins and circulation of waters through the crust. Berner and Berner [1987] give detailed analyses of these processes for a variety of chemicals. An interesting alternative we discuss later in the book (chapter 6) is that some chemicals might be controlled
Panel 1.1.1: Temporal Response of Ocean Chemistry to Perturbations
We can use the simple one-box model of the ocean represented by (1.1.8) to obtain valuable information about how ocean concentrations might respond to perturbations. One such perturbation might be a change in the rate of input by rivers associated with an increase in ice cover over land. For example, if the river flux doubled due to increased dryness and erosion during periods of glaciation and all else remained the same, (1.1.9) tells us that the
final new steady-state concentration, Coc , would be double the previous steady-state concentration, Cinitial . oc
It is also of interest to ask how this new equilibrium would be achieved. We can obtain an answer to this question by solving the time-dependent equation (1.1.8). An analytical solution exists if the change in river flux is assumed to occur instantaneously at an initial time t ¼ t0:
This equation shows that the approach to the final concentration is exponential, with the time scale determined by the rate constant k. Chemicals with a short residence time, i.e., large k, will approach equilibrium more rapidly than chemicals with a long residence time.
Another simple example for which an analytical solution is possible is one in which the source varies cyclically. Suppose, for example, that the glacial cycles have a large impact on the concentration of chemicals in rivers, and that this causes the river concentration to vary sinusoidally with time:
nriver � Criver ¼ aþb � sin ot (2)
The constant a is themean river flux, and b is the amplitude of the variation in the flux (units ¼ mol yr�1). The frequency
6
� �
Introduction
by a hybrid of the kinetic control and equilibrium mechanisms, where the removal rate is first order in the deviation of the concentration from the equilibrium concentration, i.e., R ¼ Voc � k � (Coc � Cequilibrium).
The most important message of this discussion is the crucial role of the removal mechanisms and rate constants in controlling the chemical concentration. The complexity of removal processes makes the ocean in many ways a more interesting place than if only chem
1.2 Distribution of Chemicals in the Ocean
Figure 1.2.1 is our first information about the nature of variation in space: it shows vertical profiles of various elements in the Pacific Ocean. We notice that some elements vary and others do not. Let us think first about those that do not, for example, sodium, magnesium, potassium, calcium, and rubidium, on the left-hand side; and chlorine, sulfur, and bromine on the right-hand side. In combination (and with sulfur converted to sulfate ion), elements such as these make up the vast majority of the total concentration of dissolved elements in the ocean (table 1.2.1). They are also the ones with the longest residence times (table 1.1.1). We might then think that the rate at which things happen to them is slower than the rate at which the water of the ocean mixes completely. Indeed, we shall see later in this section that the mixing time of the ocean is about one thousand years, far less than the residence time of the major constituents shown in table 1.2.1. This would explain why they are relatively uniform. Nevertheless, there are small variations in their concentration driven
o is 2p/T, where T is the period of the oscillation, for example, *100,000 years in the case of the glacial cycles. The solution to (1.1.8) for this case is:
1 a b Coc(t) ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin (ot þ f) (3)
V �
k þ p
o2 þk2 �
The first term inside the brackets shows that the mean ocean concentration is directly proportional to the mean river concentration and inversely proportional to the removal rate constant. The amplitude of the variation in ocean concentration in response to variations in the river input of the chemical is given by the second term in the brackets. This amplitude is directly related to the amplitude of the variation in the river input and inversely related to the square root of the sum of the squares of the rate constant k and the frequency of the river flux
ical equilibria controlled its composition. The geological record yields dramatic evidence of changes in oceanic composition that are consistent with the kinetic model. For example, substantial reductions in deep-sea oxygen occurred during the lower Cretaceous (125– 90 million years before present), and a major redistribution of dissolved inorganic carbon in the ocean led to a reduction of atmospheric CO2 by almost one-third during the last ice age.
primarily by evaporation and rainfall in combination with ocean circulation. These processes are discussed in chapter 2.
The distribution of the remaining chemicals is far from uniform. Most have lower concentrations at the surface than at depth, but some, such as cobalt and lead, have higher concentrations at the surface. Many processes affect the vertical distribution of such chemicals. Biological processes or chemical scavenging by sinking particles generally explain profiles with reduced surface concentrations. Profiles with higher concentrations at the surface are generally influenced by atmospheric deposition. The impact of biology on some of the elements is used by Broecker and Peng [1982] as a basis for classifying them into biolimiting elements (those such as nitrogen in the form of nitrate, phosphorus in the form of phosphate, and silicon in the form of silicic acid, whose surface concentrations are nearly depleted by biological processes, or processes associated with biology); biointermediate elements (those
variation o. The f inside the parentheses of the sine is the phase shift in the oceanic variation relative to the river variation, the value of which can be found from tan f ¼ o/k. Analysis of (3) suggests two extremes for the possible responses of the oceanic concentration to variations in river input: (a) if k is much larger than o, i.e., if the oceanic residence time is short relative to the period of the oscillation in the river input, then the amplitude of the oceanic response becomes proportional to b/k. This means that oceanic concentration, which has a mean of a/k, will vary in direct proportion to the variation in the river input. (b) If o is much larger than k, i.e., if the river concentration is varying on a time scale that is much shorter than the residence time of the chemical in the ocean, then the oceanic response to variations in river concentration will be relatively small.
waters deep in the ocean (see chapter 3) and, in the case of oxygen, by biological production as part of photosynthesis and consumption
by respiration. A few elements such as Pb have higher concentrations at the surface due to delivery by dust transport, and lower
concentrations at depth due to rapid scavenging from the water column to the sediments.
9
Chapter 1
Table 1.2.1 Concentration of major ions in seawater with a salinity of 35 Based on Table 2.3-1 of Kennish [1989]. The percent is with respect to a total mass of major ions of 35.1589 g kg�1:
Cation g kg�1 % Anion g kg�1 %
Naþ
Mg2þ
Ca2þ
Kþ
10.76 1.297 0.4119 0.399
30.60 3.69 1.17 1.13
Cl�
SO4 2�
19.353 2.712
55.04 7.71
Note: Salinity is an approximate measure of the total concentration
of chemicals in the ocean. Its original definition is the total mass in one
kilogram of seawater after all organic chemicals have been completely
oxidized, all carbonate converted to oxide, and all bromine and iodine
replaced by chlorine. The salinity defined this way is reported in units
of g salt (kg seawater)�1, for which the symbol % is used. Salinity is
now reported on the Practical Salinity Scale, which refers to a conduc
tivity ratio [UNESCO, 1985].
such as carbon and barium that are associated with biological processes, but are not limiting their rates, and therefore tend to be only partially depleted in surface waters); and biounlimited elements (those such as the major ions of table 1.2.1 that show generally uniform distributions).
For the primary example in this section, we turn to the elements that show a sharp reduction in concentration near the surface (figure 1.2.1). The obvious questions are: What causes these gradients, and why do some elements, but not all, have them? One of the main features of oceanography, and one of the main attractions of doing oceanographic research, is combining reasoning from several scientific disciplines. The following example about the control of differences between surface and subsurface concentrations shows how this happens, and in doing so serves to introduce much of the material of the book and show why it is relevant.
The key to explaining the sharp reduction in near-surface concentrations is that photosynthesis occurs in the sunlit surface ocean (figure 1.2.2). The essential effect of photosynthesis is to capture the energy from the sun and make particulate and dissolved organic matter from dissolved inorganic matter (carbon dioxide and nutrients). The organic matter that is formed can be transported downward before it is converted back into dissolved inorganic matter (remineralized). These re-mineralization processes liberate the energy contained in organic matter and provide the essential energy for the organisms that live off this organic matter. This surface production–deep remineralization loop is what causes the vertical gradients to happen. Biological production is discussed in chapter 4. One of the important messages from that discussion is that organisms utilize some chemical elements in stoichiometric (i.e., molar) ratios that can be considered nearly constant across the world. The photosynthesis and associated reactions
combine inorganic carbon, nitrogen, and phosphorus together with water to form organic matter and release oxygen. This reaction is typically represented in the following form [Anderson, 1995]:
106 CO2 þ16 HNO3 þH3PO4 þ 78 H2O
Ð C106H175O42N16Pþ150 O2
with inorganic carbon in the form of carbon dioxide, inorganic nitrogen in the form of HNO3, and inorganic phosphorus in the form of H3PO4, and organic matter of composition C106H175O42N16P. Remineralization is the opposite of this reaction, combining oxygen with organic matter to produce the inorganic chemical forms of carbon, nitrogen, and phosphorus as well as releasing energy. We will consider the inorganic concentrations of three of these elements here: phosphorus, carbon, and O2, in that order. From the above reaction, we see that the stoichiometric ratio of biological utilization and production of these three elements and nitrogen is C:N:P:O2 ¼ 106:16:1:�150, where C is in the form CO2, N is in the form of HNO3, and P is in the form H3PO4.
Spatial variations call for box models with more than one box. The minimum number that would be required to have surface concentrations lower than deep concentrations is two. We use the schematic in figure 1.2.3 as a basis for constructing a first model to represent the processes that give rise to sharp surface gradients. The schematic leaves out the river input and sediment burial fluxes considered in the previous section (figure 1.1.2); these external sources and sinks operate on much longer timescales than the interior ocean processes shown in figure 1.2.3 and can thus be safely ignored for purposes of this discussion. Water movement and the equations that govern it are complicated, but it often suffices to represent it very simply in terms of a volume exchange rate n (m3 s�1) between two well-mixed boxes. If some substance has concentrations Cs and Cd
(mol m�3) in surface and deep boxes, respectively, then there is a net exchange flux n � (Cs � Cd) mol s�1 from surface to deep.
The phosphorus balance in the deep box of figure 1.2.3 is given by:
Vd d[PO3
4�]d ([PO3
4�]s � [PO3
4�]d) þ FP (1:2:1)�
dt ¼ n �
where [PO34�] is the dissolved phosphate concentration
and FP (mol s�1) is the total surface-to-abyssal flux of organic phosphorus that is converted back into inorganic phosphorus in the deep ocean. Dissolved inorganic phosphorus exists in the ocean primarily as the phosphate ion. The organic matter flux includes sinking in the particulate form as well as volume exchange of the dissolved form, which we do not represent explicitly at this time. Note that the surface box has an equation identical to (1.2.1) except
10
Introduction
0 m
PHYTOPLANKTON
SURFACE OCEAN
THERMOCLINE AND DEEP OCEAN
BACTERIA +
ZOOPLANKTON
~100 m
TRA
NS
PO
RT
AN
D T
RA
NS
PO
RT
SE
TTLI
NG
LIGHT
DISSOLVED CO2 &
NUTRIENTS
ORGANIC MATTER &
OXYGEN
DISSOLVED CO2 &
NUTRIENTS
ORGANIC MATTER &
OXYGEN
Figure 1.2.2: A schematic illustration of the role of biology in the oceans. Phytoplankton make organic matter from
dissolved carbon dioxide and nutrients using light as a source of energy. Most of this organic matter is recycled within
the surface by phytoplankton and various other organisms such as zooplankton and bacteria (see chapter 4). Eventually
some of this organic carbon settles out or is transported below the surface ocean past a depth of about 100 m, below
which light is insufficient for photosynthesis. Biological processes in the deep ocean consume the organic matter and
oxygen, eventually converting it back into dissolved carbon dioxide and nutrients. The loop is closed by transport of these
inorganic substances back into the surface ocean.
that the terms on the right-hand side have their signs reversed, i.e., n � ([PO3
4�]d � [PO3
4�] ) � FP. The signs are s
reversed because the nutrient supply by volume exchange now brings in water with deep concentration and removes water with the surface concentration, and the flux of organic matter is out of the box. The steady-state solution to (1.2.1) is simple: the flux of organic phosphorus from the surface to the abyss is equal to the net transport of inorganic phosphorus from the abyss to the surface:
FP ¼ n � ([PO34�]d � [PO3
4�]s) (1:2:2)
Note that this equation does not say anything about the mechanism by which organic phosphorus is produced by organisms. It merely states that we can determine the flux of organic phosphorus from the surface ocean if we know n, [PO3
4�]d, and [PO3
4�]s. The concentrations are mea
sured, with deep ocean phosphate being 2.1 mmol m�3
and surface phosphate being near 0 over most of the ocean. However, this leaves us with one additional unknown, n. The equation therefore cannot be solved without an additional constraint. We can try using the
Cs
Cd
SURFACE
DEEP
Φ ν
Figure 1.2.3: Schematic of a two-box model of the ocean. The organic
matter flux F has units of mol s�1. The volumetric exchange rate
v has units of m3 s�1. We ignore river input into the surface of the
ocean and loss to the sediments, both of which are negligible
compared to the fluxes between the two boxes.
11
� �
Chapter 1
conservation equation for an additional biologically utilized element, such as carbon. The steady-state solution for the dissolved inorganic carbon (DIC ) balance gives an equation exactly analogous to that for phosphate:
FC ¼ n � (DICd � DICs) (1:2:3)
However, this new equation has also added a new unknown, the flux FC of carbon to the deep ocean. Making use of the stoichiometric ratios, i.e. FP ¼ Fc/106, enables us to solve for the concentration of carbon with
respect to that of phosphate, or vice versa, but does not give us a solution for n. The same would happen if we put down an equation for other elements that are involved in biological processes, such as oxygen.
In order to determine the magnitude of the organic matter flux, we use a tracer of ocean circulation that provides us with a time clock of the volume exchange rate n. Panel 1.2.1 shows how to calculate the exchange rate using radiocarbon, the radioactive isotope of carbon. The exchange rate we obtain is n ¼ 1.2 � 1015 m3 yr�1, i.e., 38
Panel 1.2.1: Estimation of Two-Box Model Exchange Rate Using Radiocarbon
Radiocarbon follows the same biological and mixing pathways as the stable carbon isotopes 12C and 13C,
14but decays at a known rate @14C/@t ¼�l � C, where l ¼ 1/8267 yr�1 is the decay constant of radiocarbon (the half-life is 5730 years). It is formed by cosmic ray spallation of 14N in the atmosphere and enters the surface of the ocean as 14CO2. It is the decay of this ‘‘natural’’ radiocarbon that gives us the time clock that we use in order to estimate the volumetric exchange rate between the boxes in the two-box model.
Radiocarbon is measured either by detecting the beta particles that a carbon sample of known mass produces as it decays, which is then reported as a ratio of 14C to the total carbon C in the sample, or by using a mass spectrometer to directly measure the ratio of 14C to 12C. It is reported in the literature as D14C, defined as the relative deviation in per mille from a standard sample after various corrections for fractionation effects and decay of the standard [see Stuiver and Polach, 1977]. The standard is corrected to represent the modern atmospheric radiocarbon before the industrial revolution started adding radiocarbon-depleted fossil fuel CO2 to the atmosphere and before nuclear bomb tests began enriching the atmospheric radiocarbon content. In effect, we have that
D14C ¼ 14Csample 14Cstandard
� 1 � 103 (1)
For example, typical preindustrial surface water had a D14C of �50%, which means its radiocarbon content per unit mass or volume of total carbon was 5% lower than the preindustrial atmospheric concentration as inferred from the standard.
In order to make use of radiocarbon in our box model, we need to convert the D14C units into units of 14C concentration per unit volume. We start by converting D14C into R*, defined as the ratio of the radiocarbon in the measured sample to the radiocarbon in the standard:
¼ D14C 14Csample
R * � 10�3 þ1 ¼14Cstandard
(2)
This gives R* ¼ 0.95 for the aforementioned surface water sample. In order to convert this into radiocarbon concentration in mmol m�3, we multiply it by the ratio of radiocarbon atoms to total carbon atoms that the ocean would have had if it were in equilibrium with the preindustrial atmosphere, a, and by the total concentration of carbon in the water, DIC:
DI14C ¼ a � DIC � R* (3)
The ratio a varies by only a small amount due to temperature sensitivity of air-sea fractionation effects, which we will ignore here. We thus have for the steady-state radiocarbon balance of the deep box of the two-box model that the net input of radiocarbon by vertical exchange and organic carbon input is balanced by decay of radiocarbon:
n � (DICs � Rs * � DICd � Rd
*)þFC � Rs * ¼ l � Vd � DICd � Rd
* (4)
The constant a cancels out of the equation. Note that we specify that the radiocarbon ratio of the organic carbon is the same as the surface radiocarbon ratio, since it forms by uptake of surface inorganic carbon.
The decay term on the right-hand side in (4) provides the time clock that enables us to solve for the volume exchange rate. We eliminate the organic carbon flux FC
observed value of the preindustrial surface radiocarbon
by substituting (1.2.3) into (4). This gives
l Vd� � DICd � R * d ¼ n � (DICs � R *
s � DICd � R * d)
þn � (DICd � DICs) � R * s
(5)
which can be rearranged to give
n ¼R* s R*
d � 1 � l � Vd
(6)
The deep ocean volume is about 1.26�1018 m 3 . The
ratio is 0.95 (i.e., 5% depleted with respect to the preindustrial atmosphere). The mean radiocarbon ratio of the deep ocean is 0.84. We thus obtain the solution n ¼ 1.2�1015m3 yr�1.
12
Introduction
Sverdrups (1 Sv ¼ 106 m3 s�1). The residence time of the deep ocean with respect to this exchange rate is Vd/ n ¼ 1050 years. If we divide the volume exchange rate by the area of the ocean, 3.4 � 1014 m2, we find that the mean exchange rate between the surface and deep ocean in the two-box model is about 3.5 m yr�1. We are now able to calculate additional details of the ocean cycle of nutrients and carbon. The net organic phosphorus flux from the surface to the deep ocean is
We can estimate the export of organic carbon directly from this using the molar ratio of carbon to phosphorus in organic matter of 106. Using a molecular weight of 12 g mol�1 for carbon and converting to the commonly used units of Pg C yr�1 (1 Pg ¼ 1015 g) gives a carbon export of 3.2 Pg C yr�1. More sophisticated ocean models tend to give a number three times this. A two-box model such as ours is too simple to capture all the important exchange processes.
Despite its limitations, which we shall examine in a moment, the two-box model we have developed provides powerful insights into the cycling of chemicals in the ocean. However, the two-box model gives erroneous results when applied to oxygen. Understanding why this is so will give us important additional insights into the box modeling approach and ocean biogeochemistry.
Photosynthesis produces oxygen and remineralization consumes it. The shape of the vertical profile of oxygen reflects these processes: it is lower at depth than at the surface (figure 1.2.1). The photosynthesis reaction above suggests that in these reactions, the ratio of moles of oxygen molecules (O2) to moles of phosphorus atoms appears to be roughly constant at about �150. This observation permits a powerful simplifying assumption: that 150 oxygen molecules are removed for every phosphorus atom added to the water by remineralization, i.e., FO2 ¼ �150 � FP. The oxygen box model equation for the deep ocean thus becomes:
Vd � d[O
dt 2]d ¼ n � ([O2]s � [O2]d) � 150 � FP (1:2:5)
If we assume steady state and make use of FP defined by (1.2.2), we obtain the following solution:
0 ¼ [O2]s � [O2]d � 150 � ([PO34�]d � [PO3
4�] ) (1:2:6)s
Note that the volume exchange rate n canceled out of the equation. We test the model by using it to predict the deep ocean oxygen concentration and comparing this against the observed average value of 162 mmol m�3. Rearranging (1.2.6) and substituting in the observed
mean values gives the following result:
[O2]d ¼ [O2]s � 150 � ([PO34�]d � [PO3
4�]sÞ
¼ [234 � 150 � (2:1 � 0)] mmol m�3 (1:2:7)
¼� 81 mmol m�3
The predicted concentration is negative, an impossibility. Where did we go wrong?
The answer is that we have failed to properly consider how deep water actually forms in the ocean. Most of the water sinking into the deep ocean comes from surface waters of the high latitudes. The surface waters of the high latitudes have two properties very different from the global average surface properties used in the above model. Firstly, they have much colder temperatures. Oxygen is more soluble in cold waters, therefore the oxygen concentration in the waters that sink into the deep ocean is much higher than the global surface mean, which is strongly biased by the warm waters of the low latitudes. The average surface saturation oxygen concentration in the waters that fill the abyss is about 331 mmol m�3. The actual concentration is undersaturated by perhaps 10 to 20 mmol m�3 [Najjar and Keeling, 1997], giving about 316 mmol m�3 for the water that actually sinks to the deep ocean. This increases our oxygen estimate of (1.2.7) by 82 mmol m�3. However, this still leaves us with a deep ocean oxygen of only 1 mmol m�3.
The second and most important problem with the above model is that it assumes that biological uptake keeps the surface phosphorus at a concentration that is near zero. Again, this is a reasonable assumption for the global mean surface concentration, but not at all the case in the high-latitude regions where deep water forms (see figure 1.2.4). There the biological uptake of phosphorus is not so efficient and surface concentrations of phosphorus average about 1.3 mmol m�3 [Broecker et al., 1985a].
In order to deal with the issues raised by these observations, we develop a new three-box model of the ocean that splits the surface ocean into a high latitude as well as a low-latitude box (figure 1.2.5). There are two vertical exchange terms between the surface and deep ocean. The first involves vertical exchange fhd between the high-latitude surface box and deep ocean, which is analogous to deep water formation processes that occur around the Antarctic. The second is an overturning term T of water flowing up into the low-latitude surface ocean, then towards the high-latitude surface ocean, before sinking. The overturning exchange T is analogous to the deep water formation processes that occur in the North Atlantic. A solution to the three-box model can be obtained by a procedure exactly analogous to that used in obtaining the two-box model solution. We solve for the organic matter fluxes Fh and Fl to the deep ocean using the phosphorus balance, and we use the ratio of oxygen to phosphorus in the biological reactions to substitute the phosphorus flux into the oxygen
Figure 1.2.4: Global map of the annual mean surface phosphate concentration (see also color plate 2). Note that phosphate is nearly depleted
throughout the subtropical gyres of the ocean, but that it is high in the high latitudes of the North Pacific, North Atlantic, and Southern
Ocean, as well as in the equatorial Pacific and off of southwest Africa. Data are from the World Ocean Atlas 2001 [Conkright et al., 2002].
equation for the deep ocean. The final equation for the oxygen concentration in the deep ocean is:
[O2]d ¼ [O2]h � 150 � ([PO34�]d � [PO3
4�]h)
¼ [316 � 150 � (2:1 � 1:3)] mmol m�3 (1:2:8)
¼ 196 mmol m�3
This solution is identical to the two-box model solution of (1.2.7), except that the global mean surface oxygen and phosphorus concentrations of (1.2.7) are replaced in (1.2.8) by the high-latitude mean concentrations. The higher oxygen and phosphorus concentrations in surface waters of the high latitudes give a deep ocean oxygen prediction that is now in much better agreement with the observed concentration of 162 mmol m�3. The remaining disagreement between the model prediction and observations is due in part to the fact that the organic matter that sinks into the deep ocean appears to have a composition that is rich in carbon and hydrogen. The stoichiometric ratio of oxygen consumption to inorganic phosphorus release in the deep ocean is thus closer to 170 rather than 150 [Anderson and Sarmiento, 1994]. This drops the oxygen prediction to 180 mmol m�3.
An important theme of this book is the crucial role played by the surface nutrient content of the high latitudes in controlling the chemistry of the deep ocean. The three-box model solution (1.2.8) provides an inter-
HIGH-LAT LOW-LAT
Ch Cl
T
fhd Φl
Φh Cd
DEEP
Figure 1.2.5: Schematic of a three-box model of the ocean in which the
surface waters have been divided into high-latitude and low-latitude
regions intended to represent areas where the surface nutrients tend to
be high (high latitudes) and areas where the surface concentration tend
to be low (low latitudes [cf. Sarmiento and Toggweiler, 1984]). As with the
two-box model, F (mol s�1) is the organic matter flux from the surface
boxes to the deep box. The volumetric exchange rates (m3 s�1) between
boxes consists of mixing fhd between the high-latitude surface box and
deep ocean, and an overturning circulation T, which flows from the
deep ocean into the low-latitude surface and then through the high-
latitude surface box back into the deep box.
14
Introduction
esting, though oversimplified, illustration of the potential importance of this process. It suggests that the oxygen content of the deep ocean has the potential to vary between 0 and 316 mmol m�3 with changes in the surface phosphate concentration of the high latitudes of between 0.24 and 2.1 mmol m�3. This sensitivity was exploited by Sarmiento et al. [1988a] to provide a hypothesis for the cause of episodes of deep ocean anoxia (total depletion of oxygen) that have been observed in the geological record of the ocean sediments. If, for example, the high-latitude phosphate were to drop, then (1.2.8) suggests that the deep ocean oxygen should also drop.
However, in subsequent work with more sophisticated three-dimensional models of ocean circulation
1.3 Chapter Conclusion and Outline of Book
The central concern of this book is to understand the processes that control the mean oceanic concentration as well as the spatial and temporal variations of chemicals that are influenced by biological processes. As illustrated by the box models, this requires understanding the transport of chemicals by processes such as advection and diffusion. It also requires us to understand sources and sinks of the chemicals, such as biological uptake and remineralization, as well as boundary conditions at the surface and bottom of the ocean such as gas exchange and sediment water fluxes.
The view taken in what follows is that kinetic processes are the primary control on the composition of the ocean, as proposed by Broecker’s response to Sillen’s equilibrium view [Broecker, 1971]. This view was explored in detail in the book Tracers in the Sea that Broecker wrote with Peng in 1982. The progress since then, and recent completion of several global measurement and modeling programs, suggests the need for a new look at what we have chosen to call ‘‘ocean biogeochemical dynamics.’’ This title recognizes the important role of biological and geological, as well as chemical, processes, in controlling the oceanic composition of the chemicals we will study here, as well as the fact that these phenomena show considerable change through time.
We begin in chapter 2 with a derivation of the tracer conservation equation and a review of our understanding of ocean transport by advection and mixing. Subsequent chapters will go through each of the other processes that must be specified in order to solve the tracer conservation equation. Boundary conditions must be given at the air-sea interface and at the ocean floor. Among the boundary processes that must be considered are gas exchange at the air-sea interface, and fluxes from the sediments resulting from reactions in the sediments. We must also consider sources and sinks inter-
consisting of tens of thousands of boxes, it was found that the sensitivity of the deep ocean oxygen to high-latitude nutrients was much smaller than predicted by the three-box model [Sarmiento and Orr, 1991]. The three-dimensional models lose only 41 mmol m�3 of oxygen when nutrients are reduced to zero, as contrasted with the loss of more than 180 mmol m�3 that our box model gives. The three-dimensional models confine the reduction of deep ocean oxygen to regions just below the high-latitude deep water formation regions so that the average deep ocean oxygen drops only modestly. This and the previous examples demonstrate clearly the importance of understanding ocean transport and of understanding how to develop box models that can represent the circulation realistically.
nal to the ocean due to chemical and biological processes. Chemical processes will not be dealt with as a separate topic, but rather will be brought into the discussion whenever relevant, primarily as part of the examples.Biological processes canremove inorganic chemicals by photosynthesis, which uses light as a source of energy, or chemosynthesis, which uses chemical reactions as a source of energy. The major region where this occurs is in the euphotic zone at the surface of the ocean, where light is sufficient to support photosynthesis. Biological processes also add inorganic chemicals by re-mineralization of organic matter. This occurs at all depths in the ocean as well as in the sediments.
We cover each of these topics beginning at the surface and moving down through the water column into the sediments. Chapter 3 deals with boundary conditions at the air-sea interface. Chapter 4 covers the formation of organic matter in the surface ocean. Chapter 5 covers the transport of organic matter from the surface to the abyss and its remineralization at depth. Chapter 6 covers the ocean sediments. The emphasis of these chapters is on the chemical cycles of the major nutrients (nitrate and phosphate) and oxygen.
After developing a deeper understanding of relevant oceanic processes as well as the cycling of the major nutrients and oxygen, we apply this understanding to an analysis of the chemical cycles of silicon in chapter 7 and carbon in chapter 8, and of CaCO3 in chapter 9. Finally, chapter 10 applies the tools developed in chapters 1 through 9 to a discussion of three of the major outstanding problems in our understanding of the influence of the ocean on atmospheric carbon dioxide. These are the role of the ocean as a sink for anthropogenic carbon, in the interannual variability of atmospheric carbon dioxide, and in the large reductions of atmospheric carbon dioxide that occurred during ice ages.
15
Problems
1.1 Explain in words why we think that neither the accumulation hypothesis nor the equilibrium control hypothesis is correct for explaining the huge variations that we observe for the mean oceanic concentration of the different elements in the ocean.
a. Describe the test that we devised for the accumulation hypothesis and what information we used to reject this hypothesis.
b. Do the same for the equilibrium hypothesis.
1.2 If we nevertheless accept the hypothesis that the mean concentration of elements in the ocean is a result of the accumulation from river input, how large would today’s ocean concentration be of magnesium, arsenic, chlorine, and gold? (Use an ocean age of 3.85 billion years and the river concentrations given in table 1.1.1).
1.3 List two elements that fall into each of the following categories: biolimiting, biointermediate, and biounlimited. Explain the basis of your choice.
1.4 During photosynthesis, how many free oxygen molecules are produced per nitrogen atom consumed? How many free oxygen molecules are produced per carbon atom consumed?
1.5 Equation (1.2.2) tells us that, at steady state, the upward supply of nutrients has to be balanced by the downward flux of nutrients in organic matter.
a. Discuss how the biological export production would change if the deep and surface concentrations were suddenly halved.
b. Discuss how biological export production would react to a sudden doubling of the vertical exchange rate n.
1.6 Describe what would happen in the one-box model if the concentration of phosphate in the ocean was suddenly doubled, but the river input and removal rate constant k remained the same. Describe first the final steady state, and then the time it would take to achieve the final steady state.
1.7 What would happen to the global mean oceanic phosphate concentration if the river concentration of phosphate in the one-box model were suddenly to double? Draw a graph of concentration versus time, showing the behavior in time as well as the final concentration. Assume that phosphate removal is first order.
16
� �
Introduction
a. Solve first for steady state. Then draw the solution at t ¼ 0 and at t ¼ ?.
b. Solve for the time-dependence. Use the solution given in panel 1.1.1. Add the time-dependence to the figure.
c. Discuss what determines the response time of the ocean.
1.8 Suppose that the input of a chemical to the ocean were to vary sinusoidally with a frequency o of 2p/100,000 yr�1 and an amplitude equal to 50% of the mean input. What is the ratio of the amplitude in the oceanic concentration variation to the mean oceanic concentration for Mg and Si? (Assume that removal for both is first order and that the mean life for each is as given by table 1.1.1.)
1.9 Suppose that the removal rate for a substance A is second order in the concentration of A and B, i.e., RA ¼ V � k1 � [A] � [B]. Such might be the case if A were removed from the ocean by precipitation as the mineral AB. Suppose further that B is removed both by precipitation with A, but also by a separate first-order removal process, such that RB ¼ V � k1 � [A] � [B] þV k2 [B].
a. Derive an equation for the steady-state concentrations of A and B.
b. Show the approximate solution for the case where the river concentration of B is much greater than the river concentration of A. Compare this solution with the solution for first-order removal.
1.10 The water sinking into the deep box of the two-box model comes primarily from high latitudes. Suppose that the water sinking from the high latitudes has a radiocarbon ratio Rs* of 0.92 but that everything else is as in the two-box model discussed in panel 1.2.1.
a. What is the volume exchange rate between the deep and shallow boxes?
b. The shallow box has a thickness of 100 m and the deep box a thickness of 4000 m. What is the residence time of the surface box with respect to exchange with the deep box? What is the residence time of the deep box with respect to exchange with the surface box?
c. How large is the biological export production in this case (in units of carbon, e.g., Pg C yr�1)?
1.11 Consider an element C that is transported to the surface in the two-box model, where g is the fraction of upwelled nutrients that is converted to organic matter and then carried into the deep ocean.
a. Derive an equation for g in terms of the surface and deep ocean concentrations.
b. Calculate the magnitude of g for the following elements using the data in table 1.1.1 for the deep ocean concentration, and the following surface concentrations.
Cs (mmol m�3)
P 0.1 Ba 0.026 Ca 10,251
17
Chapter 1
1.12 Add the river flux and sediment burial terms of figure 1.1.2 to the box model of figure 1.2.3. River delivery occurs into the surface box. Assume that the sediment burial flux is a fraction f of the organic matter flux F.
a. Derive an equation for f. Start with the conservation equation for surface and deep boxes, and then assume steady state.
b. Use the equation in (a) in combination with the information in problem 1.11 and table 1.1.1 to determine the magnitude of f for P, Ba, and Ca.
c. Discuss the solution. Is it realistic? Can you explain the differences between the three elements?
1.13 Show how to derive equation (1.2.8). Start with the conservation equation for the deep box for phosphorus and oxygen. Note that low-latitude surface phosphate is 0 and that FO2 ¼ rO2:P � FP, where rO2:P is �150. Assume steady state and solve for deep O2.
1.14 Suppose the deep phosphate concentration doubled due to an increase in the river flow.
a. How would this affect the deep ocean oxygen concentration if high-latitude phosphate remained the same?
b. How would this affect the deep ocean oxygen concentration if the high-latitude phosphate concentration also doubled?
